Quantum geometry, matrix theory, and gravity / Harold C. Steinacker.

Format:

Book

Author/Creator:

Steinacker, Harold C., 1968- author.

Language:

English

Subjects (All):

Geometric quantization.

Gravity--Mathematical models.

Gravity.

String models.

Matrices.

Physical Description:

1 online resource (xvi 402 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2024.

Summary:

"Building on mathematical structures familiar from quantum mechanics, this book provides an introduction to quantization in a broad context before developing a framework for quantum geometry in Matrix Theory and string theory. Taking a physics-oriented approach to quantum geometry, this framework helps explain the physics of Yang-Mills-type matrix models, leading to a quantum theory of space-time and matter. This novel framework is then applied to Matrix Theory, which is defined through distinguished maximally supersymmetric matrix models related to string theory. A mechanism for gravity is discussed in depth, which emerges as a quantum effect on quantum space-time within Matrix Theory. Using explicit examples and exercises, readers will develop a physical intuition for the mathematical concepts and mechanisms. It will benefit advanced students and researchers in theoretical and mathematical physics, and is a useful resource for physicists and mathematicians interested in the geometrical aspects of quantization in a broader context"-- Provided by publisher

Contents:

Differentiable manifolds

Lie groups and coadjoint orbits

Quantization of symplectic manifolds

Quantum spaces and matrix geometry

Covariant quantum spaces

Noncommutative field theory

Yang-Mills matrix models and quantum spaces

Fuzzy extra dimensions

Geometry and dynamics in Yang-Mills matrix models

Higher-spin gauge theory on quantum spacetime

Matrix theory : maximally supersymmetric matrix models

Gravity as a quantum effect on quantum spacetime

Matrix quantum mechanics and the BFSS model

Notes:

Title from publisher's bibliographic system (viewed on 04 Apr 2024).

ISBN:

9781009440806

1009440802

9781009440776

1009440772

OCLC:

1428420316